An Analysis of Algorithmic Components for Multiobjective Ant Colony Optimization: A Case Study on the Biobjective TSP

  • Manuel López-Ibáñez
  • Thomas Stützle
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5975)

Abstract

In many practical problems, several conflicting criteria exist for evaluating solutions. In recent years, strong research efforts have been made to develop efficient algorithmic techniques for tackling such multi-objective optimization problems. Many of these algorithms are extensions of well-known metaheuristics. In particular, over the last few years, several extensions of ant colony optimization (ACO) algorithms have been proposed for solving multi-objective problems. These extensions often propose multiple answers to algorithmic design questions arising in a multi-objective ACO approach. However, the benefits of each one of these answers are rarely examined against alternative approaches. This article reports results of an empirical research effort aimed at analyzing the components of ACO algorithms for tackling multi-objective combinatorial problems. We use the bi-objective travelling salesman problem as a case study of the effect of algorithmic components and their possible interactions on performance. Examples of design choices are the use of local search, the use of one versus several pheromone matrices, and the use of one or several ant colonies.

Keywords

Multiobjective Optimization Ant Colony Optimization  Travelling Salesman Problem 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Alaya, I., Solnon, C., Ghédira, K.: Ant colony optimization for multi-objective optimization problems. In: 19th IEEE International Conference on Tools with Artificial Intelligence (ICTAI 2007), Los Alamitos, CA, vol. 1, pp. 450–457. IEEE Computer Society Press, Los Alamitos (2007)CrossRefGoogle Scholar
  2. 2.
    Angus, D.: Population-based ant colony optimisation for multi-objective function optimisation. In: Randall, M., Abbass, H.A., Wiles, J. (eds.) ACAL 2007. LNCS (LNAI), vol. 4828, pp. 232–244. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  3. 3.
    Angus, D., Woodward, C.: Multiple objective ant colony optimization. Swarm Intelligence 3(1), 69–85 (2009)CrossRefGoogle Scholar
  4. 4.
    Barán, B., Schaerer, M.: A multiobjective ant colony system for vehicle routing problem with time windows. In: Proceedings of the Twentyfirst Iasted International Conference on Applied Informatics, Insbruck, Austria, pp. 97–102 (2003)Google Scholar
  5. 5.
    Doerner, K., Gutjahr, W.J., Hartl, R.F., Strauss, C., Stummer, C.: Pareto ant colony optimization: A metaheuristic approach to multiobjective portfolio selection. Annals of Operations Research 131, 79–99 (2004)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Dorigo, M., Stützle, T.: Ant Colony Optimization. MIT Press, Cambridge (2004)MATHGoogle Scholar
  7. 7.
    García-Martínez, C., Cordón, O., Herrera, F.: A taxonomy and an empirical analysis of multiple objective ant colony optimization algorithms for the bi-criteria TSP. European Journal of Operational Research 180(1), 116–148 (2007)MATHCrossRefGoogle Scholar
  8. 8.
    Grunert da Fonseca, V., Fonseca, C.M., Hall, A.O.: Inferential performance assessment of stochastic optimisers and the attainment function. In: Zitzler, E., Deb, K., Thiele, L., Coello Coello, C.A., Corne, D.W. (eds.) EMO 2001. LNCS, vol. 1993, pp. 213–225. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  9. 9.
    Hoos, H.H., Stützle, T.: Stochastic Local Search—Foundations and Applications. Morgan Kaufmann Publishers, San Francisco (2005)MATHGoogle Scholar
  10. 10.
    Iredi, S., Merkle, D., Middendorf, M.: Bi-criterion optimization with multi colony ant algorithms. In: Zitzler, E., Deb, K., Thiele, L., Coello Coello, C.A., Corne, D.W. (eds.) EMO 2001. LNCS, vol. 1993, pp. 359–372. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  11. 11.
    López-Ibáñez, M., Paquete, L., Stützle, T.: Hybrid population-based algorithms for the bi-objective quadratic assignment problem. Journal of Mathematical Modelling and Algorithms 5(1), 111–137 (2006)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    López-Ibáñez, M., Paquete, L., Stützle, T.: On the design of ACO for the biobjective quadratic assignment problem. In: Dorigo, M., Birattari, M., Blum, C., Gambardella, L.M., Mondada, F., Stützle, T. (eds.) ANTS 2004. LNCS, vol. 3172, pp. 214–225. Springer, Heidelberg (2004)Google Scholar
  13. 13.
    López-Ibáñez, M., Paquete, L., Stützle, T.: Exploratory analysis of stochastic local search algorithms in biobjective optimization. In: Bartz-Beielstein, T., et al. (eds.) Experimental Methods for the Analysis of Optimization Algorithms. Springer, Heidelberg (2010) (to appear)Google Scholar
  14. 14.
    Lust, T., Jaszkiewicz, A.: Speed-up techniques for solving large-scale biobjective TSP. Computers & Operations Research (2009) (in press)Google Scholar
  15. 15.
    Paquete, L., Stützle, T.: A study of stochastic local search algorithms for the biobjective QAP with correlated flow matrices. European Journal of Operational Research 169(3), 943–959 (2006)MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Paquete, L., Stützle, T.: Clusters of non-dominated solutions in multiobjective combinatorial optimization: An experimental analysis. In: Barichard, V., et al. (eds.) Multiobjective Programming and Goal Programming: Theoretical Results and Practical Applications. Lecture Notes in Economics and Mathematical Systems, vol. 618, pp. 69–77. Springer, Berlin (2009)Google Scholar
  17. 17.
    Stützle, T.: ACOTSP: A software package of various ant colony optimization algorithms applied to the symmetric traveling salesman problem (2002), http://www.aco-metaheuristic.org/aco-code
  18. 18.
    Stützle, T., Hoos, H.H.: \(\cal MAX\)\(\cal MIN\) Ant System. Future Generation Computer Systems 16(8), 889–914 (2000)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Manuel López-Ibáñez
    • 1
  • Thomas Stützle
    • 1
  1. 1.IRIDIA, CoDEUniversité Libre de BruxellesBrusselsBelgium

Personalised recommendations